Solve for $x$ and $y$ using elimination. $\begin{align*}-6x+y &= 7 \\ -x-y &= 1\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-7x = 8$ Divide both sides by $-7$ and reduce as necessary. $x = -\dfrac{8}{7}$ Substitute $-\dfrac{8}{7}$ for $x$ in the top equation. $-6( -\dfrac{8}{7})+y = 7$ $\dfrac{48}{7}+y = 7$ $y = \dfrac{1}{7}$ $y = \dfrac{1}{7}$ The solution is $\enspace x = -\dfrac{8}{7}, \enspace y = \dfrac{1}{7}$.